A conventional blind rivet fastening has a tubular shank with an external flange at one end, and a stem extending through the shank. A first end of the stem protrudes from the flanged end of the shank, and a second end of the stem has a head whose outer diameter corresponds to the outer diameter of the shank, and which abuts the end of the shank remote from the flange. To join two sheets of material together with the rivet, aligned holes with a diameter corresponding to the external diameter of the shank are formed in the sheets, and the shank is inserted through the aligned holes until the flange rests on one of the sheets of material. Holding the flange of the shank in this position, a tensile force is applied to the stem so that the head of the stem applies compression to the tubular shank. Depending on the geometry of the head and the shank, the head may be pulled into the shank while the wall of the shank is deformed outwardly to a greater diameter, or the head may remain at the end of the shank and the wall of the shank may buckle outwards. Tensile force is applied to the stem until, at a predetermined maximum force, the stem breaks off. The head of the stem is either retained within the shank, or may fall away after the stem breaks.